Question

What is the value of least count of commonly available Vernier callipers?
(A) \[0.01\,{\text{cm}}\]
(B) \[0.1\,{\text{cm}}\]
(C) \[1\,{\text{cm}}\]
(D) \[1\,{\text{mm}}\]

Answer 1

Hint: Use the formula for the least count of an instrument. This formula gives the relation between the main scale reading of the instrument and the total number of divisions on the secondary scale. Check the main scale reading and total number of divisions on the vernier callipers.

Formula used:
The formula for the least count of an instrument is given by
\[{\text{Least count}} = \dfrac{{{\text{Main scale reading}}}}{{{\text{Total number of divisions on secondary scale}}}}\] …… (1)

Complete step by step answer:
A commonly available Vernier scale has a main scale and a Vernier scale.The main scale reading of such commonly available Vernier callipers is \[1\,{\text{mm}}\].The total number of divisions on the vernier scale are 10.We can determine the least count of a vernier calliper using the formula given in equation (1).Rewrite equation (1) for the least count of vernier callipers.
\[{\text{Least count}} = \dfrac{{{\text{Main scale reading}}}}{{{\text{Total number of divisions on vernier scale}}}}\]
Substitute \[1\,{\text{mm}}\] for \[{\text{Main scale reading}}\] and \[{\text{10}}\] for \[{\text{Total number of divisions on vernier scale}}\] in the above equation.
\[{\text{Least count}} = \dfrac{{1\,{\text{mm}}}}{{{\text{10}}}}\]
\[ \Rightarrow {\text{Least count}} = 0.1\,{\text{mm}}\]
Hence, the least count of a commonly available Vernier caliper is \[0.1\,{\text{mm}}\].
Convert the unit of the least count of the Vernier callipers in centimeters.
\[{\text{Least count}} = \left( {0.1\,{\text{mm}}} \right)\left( {\dfrac{{{{10}^{ - 1}}\,{\text{cm}}}}{{1\,{\text{mm}}}}} \right)\]
\[ \therefore{\text{Least count}} = 0.01\,{\text{cm}}\]

Therefore, the least count of a commonly available Vernier caliper is 0.01 cm.

Additional information:
The least count of an instrument is defined as the least or minimum value which the instrument can measure with precision.The value of the least count gives the information that which instrument should be used to measure a particular length or directly measurable physical quantity.

Note:The students may get confused that the obtained least count of the vernier callipers which is \[0.1\,{\text{mm}}\] is not given in the given options. Don’t forget to convert the unit of this least count in centimeters. In such situations, students should check for the other options by converting it in other units.